Hi Lars,
The best way to achieve this is by using the "canStart" attribute on tasks. Once all predecessors have been completed, the task will show canStart=True. Or it will show False if there are still predecessors outstanding.
Using this attribute you could build a report to show all tasks assigned to a user / team, but add a filter to the report to show only tasks where canStart=True. This way the report will only show tasks that are ready to be worked on and all predecessors are met.
You can learn more about the canStart attribute here.
Best Regards,
Rich